So there are a few issues to clarify here, but first, a disclaimer: I am not an expert on the law, and will not be speaking from the point of view of interpreting the law.
That said, however, it does seem to me that an "age of consent" is an appropriate legal construct. The idea is that 13-14 year old children have simply not developed far enough, not just morally, but most importantly neurologically, to be very good yet at forecasting consequences of their actions. With respect to issues like sex, it is not unreasonable to think that if young teenagers are not yet capable of forecasting consequences of their actions--by which I mean not just being able to think or say, "I might get pregnant," or "I could catch some STD," but actually appreciate what such an outcome would mean for them--then they are reasonably thought not to have what it takes to give genuine (i.e. morally significant) consent. Of course, many girls that age know about sex, and some even have sexual fantasies. Some, given the opportunity to do so, would also agree to have sex with someone they were interested in. But such understanding, desire, and agreement cannot count as consent in the morally significant way, so long as they are incapable of really appreciating what they are (or might be) getting themselves into in terms of consequences.
This same reasoning applies to age-limits for signing legal contracts, drinking alcohol, smoking products, driving, enlisting in the military, and voting, just to name a few. The age limits are different for some of these, but the basic reasoning is similar in all cases: we think that such activities require certain levels of responsibility about consequences, and we think that below certain ages, it is not reasonable to think that young people can be responsible in the appropriate way.
By the way, I think what you say about boys is simply mistaken. An adult woman (no less than a man) who has sex with a 13- or 14-year old boy would commit statutory rape under the law. The issue is not whether or not 13- or 14-year old children are capable of having sex (physically). I assume most are. But that's not the issue and besides the point, which, again, has to do with being able to manage responsibility.
The term "child abuse" is loaded enough that I'm going to set it aside. And I'm going to restrict myself mainly to one point.
You seem to assume that religion is always a matter of "blind faith" and that if parents bring their children up in a religious tradition, this is inevitably a matter of "programming." But why think that? Isn'tit possible that perhaps you've been a bit indoctrinated (not to say brainwashed) on that point yourself?
Some beliefs are blind. That applies to some cases of religious belief and to a good many other kinds of belief as well. But not all beliefs about matters that go beyond the facts need be blind, and this is as true for religion as it is for anything else. The great religious traditions include traditions of argument, reflection, weighing of considerations, and discernment. Not all believers cling to their beliefs for dear life; not all believers believe that they're bound for hell if they have questions or doubts. In fact, for some serious religious people, detailed beliefs about difficult matters of metaphysics aren't what matters for them.
Are some forms of religious belief regrettable or worse? No doubt. The same goes, of course, for some political, ideological and moral beliefs. Do some people hold their religious views mainly out of habit? Indeed. Are some afraid to question what they've been told? Unfortunately true. Bringing up a child so that her beliefs are of that sort is a bad thing, whether the beliefs are specifically religious or not. But an unprejudiced look at the religious landscape will make clear that religion needn't be that way and frequently isn't.
Good questions, ones that are receiving more philosophical treatment recently. As a parent of three I better have some good answers, eh?
First off, I haven't read either the Stanford Encyclopedia of Philosophy (SEP) entry on Parenthood and Procreation or the book Why Have Children? by Christine Overall (see this article), but you might find those interesting.
So, here are five reasons that I think are good reasons to have children, though of course, they might be outweighed by other reasons (such as worries about overpopulation, or lacking financial resources to raise children well, etc.):
1. Human life has value and humans create valuable and meaningful things (such as art, philosophy, humor, and pleasure), so it is good for humans to continue to exist. So, someone should have kids. It might not be necessary for me or you to have children, but assuming it is better for there to be humans than not (and I think it is), then it is necessary for some people to have children. (Also, a younger generation is required to sustain the economy. You won't get social security unless enough people have kids to pay taxes when you are old.)
2. The relationship between parents and children can be a wonderful relationship that adds meaning and pleasure to one's life (yeah yeah, also frustration and pain), so if you have good reason to think your own life and that of your children will gain meaning, value, pleasure, etc. from that relationship, one should have kids. Children can be fun!
3. Children can provide you with grandchildren, which may provide all the good things described in 2 with less of the frustration and pain. At least that's what all my kids' grandparents say.
4. Children can provide you with a way to continue your existence in certain ways, both biological and psychological. (I'll leave it vague, hoping people will fill in the idea in a better way than I could in a brief response!)
5. Teaching has value and gives meaning to one's life. Passing on good ideas, beliefs, capacities, crafts, trades, traits, etc. is both necessary to sustain them and satisfying in its own right. (This may be a specific part of 1 and 2, but when I said I'd give 5 reasons I was just setting a goal for myself...)
Notice that almost none of the reasons I've given require having biological children rather than adopting. Indeed, it is harder to give reasons for why one should procreate, even if one thinks raising children has value. You may want to check out some of the discussions on this question under the "Children" category on the left bar.
Hope this helps!
Most of these questions are not so much philosophical as empirical, and there has been a tremendous amount of extremely important work done in the last few decades on children's concepts of number. The locus classicus is The Child's Understanding of Number, by Rachel Gelman and Randy Galistel, which was originally published in 1978, but this stuff really took off in the late 1990s or so. A lot of people have contributed to this work, but I'll mention two: Susan Carey and Liz Spelke, who are both at Harvard. You will find links to some of their work on their websites. Part of the reason people got interested in these issues is because they are closely related to issues about object recognition and individuation, which had been a focus of a great deal of work just before that. (I.e, people had been interested in the question at what age children start to "pick out" objects from the environment, and to think of them as distinct entities, that continue to exist even when you do not see them. The answers turn out to be every bit as fascinating as one might hope they would be.)
It turns out that there are several different cognitive systems at work in numerical cognition. One of them is system that works by "pattern recognition". This is the system that your child is using when she just "sees" how many things there are. She's not counting, even to herself, but just recognizing a pattern. Unsurprisingly, this system does not work for very large numbers. If I remember right, it tends to give out around four or five, for most people---and for many animals, too, who share this particular system with us. There's another system that is based on what people call an "analog accumulator" and that, again, we share with many other animals.
Counting, on the other hand, is something that seems found, in nature, at least, only in humans, though I know there are parrots who have been taught to count. Before we talk about counting, though, we need to distinguish two kinds of counting, which are known as "intransitive" and "transitive". (I think the terms originated with Charles Parsons, but I'm not sure.) Intransitive counting is just rehearsing the number sequence, i.e., saying, "1, 2, 3, 4", etc. Transitive counting is using the number sequence to count some objects. Obviously, you have to learn the former before you can learn the latter, and there is almost always a developmental stage where children are good enough at intransitive counting, but quite bad at transitive counting, or even unwilling to do it entirely.
We also need to distinguish the question, "Can so-and-so count transitively?" from the questions (a) how well they do it and (b) whether they understand what they are doing in the way we do. Concerning (a), the distinction we need to make here is Chomsky's distinction between "competence" and "performance". It sounds, from your description, as if your child knows that each item is to be counted (that is, "tagged" with a counting word) once and only once. But knowing this is one thing, and being able to tag each thing just once is another thing. Even we adults make this kind of mistake sometimes, and even a child who almost always makes such a mistake might know what she is supposed to be doing. So in that sense, she might be able to count, but not exhibit this ability in her performance.
Concerning (b), we adults use counting to find out how many things of a certain sort there are, a fact we then use to make other kinds of decisions. If we count five plates and then go to get forks, we also count out five forks, for the obvious reason that this is one way to make sure we have the same number of forks as plates. But there is, again, almost always a developmental stage at which children can count, but they do not understand the significance of the exercise. So if you ask them to count the plates and then go get five forks, they have no idea what to do. Indeed, at this sort of stage, children almost seem to understand the question, "How many plates are there?" as meaning: Would you please count the plates? You can ask them over and over, and they'll count each time; they won't just think, well, I just counted, so there are five, and why are you asking me again? Nor do they understand, e.g., that, if there are five dolls and five hats, then this means that you have a hat for each doll, but no more, or, conversely, that if you have five dolls and a hat for each doll, but no more, then you have five hats. Amusingly, children at this stage will very often use other "count sequences" instead of number words. They'll count "a, b, c" or "Monday, Tuesday, Wednesday", and be perfectly fine with that. The moral of the story, then, is that the ability to count does not, by itself, imply having an adult understanding of "how many" questions and their answers.
So, does your child know how to count? In some ways, yes, and in some ways, perhaps no.
There is an old saying (I'm told it originates with Kant, but I am not sure about that), which goes, "'ought' implies 'can.'" The idea is that you can only be held responsible or have an obligation to do something (you "ought" to do it) if it is something that is under your control. Do you suppose that emotions (such as love) are under one's voluntary control? I'm inclined to doubt that (with a few reservations, which I will get to momently). But if love is not something that you can voluntarily control, then it makes no sense to say that you have an obligation to love your mother (or anyone else, for that matter).
On the other hand, we do also evaluate people on the basis of how they feel about things, and on the basis of emotions they have and display. We same that some anger, for example, is inappropriate, and we regard most examples of hatred as at least unfortunate, if not contemptible. Does this make sense? I think it does make some sense, in that at least one of the things we value (positively or negatively) in people are their characters, and this includes emotions and such. So does this violate "ought" implies "can"? That seems to me to be more complicated, because while it does seem implausible to say that we can turn emotions on and off like faucets, it also seems plausible to say that the sorts of characteristics we have are at least to some extent the result of things we are able to do--for example, we can train ourselves to improve upon the way we might react to certain things (go to anger management therapy, for example, or biting our tongues when we feel impulses to say things that are cruel or hateful). people who have (or display) bad character may not be able to act any differently at the moment, but it still makes sense for us to hold them responsible for not having done the character-building that would have made them better people who would not have behaved so badly in that moment.
So back to loving your mother. On the one hand, if what you find unlovable about her are her values, it could well be that your reaction is simply the right one. There may be some respect(s) in which one need to respect and recognize the special relationship of parent and child, but I can't see why someone who is a bad person deserves to be loved by anyone, child or otherwise. On the other hand, before you take this as an excuse, you might do some serious double checking on your own values, which are leading you to reject hers. All I can know for sure, if yours and hers conflict, is that at least one of you is wrong. It might not be her, and it also might be both of you!
I suppose the ideal is that love between a parent and a child is sustained quite naturally, and is actually deserved in both cases. But maybe that is not going to be possible in this case. If so, then as I said, there are still some reasonable constraints about how you should respond to your mother (because she is your mother), having to do with civility and respect for her role in your life. There are certain duties and kinds of loyalties that we reasonably expect along these lines (though as I have already indicated, these are defeasible, if those to whom we normally would supply these have violated the ground for such things badly enough--an abusive parent, for example, may reasonably be thought to have lost any claim even on the most basic forms of loyalty from the child he or she has abused). At the very, very least, your mother deserves from you the kind of civil and polite responses you would provide as a matter of common decency.
But I can't help but wonder if perhaps you can do better than this. I don't know your mother or her values that you object to. But I suspect that civil discussion and allowing her to explain those values to you, and why they are important to her might at least allow you to achieve a level of understanding that would allow you to be more tolerant. Tolerance is not the same as love, I agree, but it's a start!
It's hard, in general, to 'blame' children for anything, being not yet responsible and beneath the 'age of reason' ... but perhaps we might blame their parents for allowing them to learn about such things and engage in them? Perhaps -- but as the father of three small boys who turn every toy into a weapon, whose favorite form of play is 'fighting bad guys' (which often include each other), it's hard to imagine STOPPING this behavior. We do our best to shield them from it, but it's everywhere -- in kid's programming, in kid's toys, in kids' lunchbags's patterns, and in their peers at school -- you cannot shut it out, short of homeschooling and utter social isolation. So I'm not sure one can blame the parents much, either .... (and perhaps one ought to focus on restraining/steering the behavior: i.e. make sure they understand it is just play, and you cannot REALLY hurt someone, and perhaps promote the creative/fantasy elements of it .....?)
I don't see what is wrong with doing things that you want to do in a case like this. One is not perpetually obliged to think of whether one could be doing more for people. Right now instead of responding to this query I might be more suitably employed doling out food for the homeless and the computer on which I am now typing could be sold to provide water for villages in the developing world which require it. I could right now be doing things that save lives, yet here I am selfishly typing away unnecessarily and satisfying my desire to make my opinions public.
To allow all my personal interests to be submerged under the interests of others, though, is to dissolve one's personality. For some of course taking this step is in fact a reflection of their personality, but in the example you say you want to bring your children up in a house with a yard. We are not under the obligation to be saints and there is no reason why you should feel guilty about the reasonable ambition to own a yard.
I wonder, because it might be argued that in general people would be expected to know the national anthem, and while provision should be made for those who do not wish to, it would be a shame if no-one could sing it at school. After all, it is not as though singing it is likely to coerce one into patriotic feelings that one would be better without, or even better with, since as we know however people are brought up often has very little to do with how they eventually behave or what they believe.
I used to teach in a school where a small group of students had to be removed from the classroom whenever Christmas was discussed, since it was held to be a largely secular holiday and they were the children of committed Christians who disapproved of this secularity. Should one have just not spoken about Christmas at all in order not to exclude them? How about if some parents object to music or sex education, should teachers not play music or provide sex education at all?
Exclusion is not desirable, but it preserves some balance between the wishes of individual parents and the desire of the education system to introduce children to central aspects of their culture, surely a worthwhile aim on the whole.